tant factor in teaching this way, Ms.
Rhea says. What’s more critical is
teaching and testing a set of basic
principles of differential calculus
that are articulated in a test called a
calculus concept inventory. This 22-
question test focuses not on whether
students can run through calculations but on whether they understand
the underlying concepts.

“It’s easy to measure if they cantake derivatives out the wazoo,” Ms.Rhea says, “but it’s kind of harderto see what they’re getting under-neath.”Research by Ms. Rhea and twocolleagues suggests that Michigan’steaching methods have led to greatergains in conceptual understanding.The techniques have been lauded bythe Association of American Uni-versities, among others.

In 2008, Michigan gave concept
inventories to students before they
started calculus and after they finished, and calculated the difference
relative to the maximum gain they
could have made. Students in Michigan’s flipped courses showed gains
at about twice the rate of those in
traditional lectures at other institutions who took the same inventories.

The students at Michigan who
fared worst—a group of 12 who
were at risk of failing the course—
showed the same gain as those who
demonstrated the largest increase in
understanding from traditional lectures elsewhere.

that model is making less sense assources of information grow moreplentiful. “Simply transmitting in-formation should not be the focus ofteaching; helping students to assimi-late that information should.”At the conference, he demonstrat-ed how his methods help studentsabsorb information and transferconcepts. He briefly explained an as-pect of thermodynamics: When mol-ecules are heated, they move awayfrom one another.After asking if there were anyquestions on this concept, he toldthe attendees to pick up their elec-tronic “clickers” to answer a ques-tion. It was not a simple test of com-prehension; he asked people to applythe concept to a new context.

The attendees entered their answers on their clickers. Mr. Mazur
told them to find someone sitting
near them who had chosen a different answer and try to persuade them
that their answer was correct. The
room quickly grew noisy.

I answered that the gap would getsmaller, figuring that the materialwould melt and the hole would startto close. Behind me, a psychologistexplained how he thought it wouldremain the same because the inter-play between the expanding metaland the air in the middle would bal-ance each other. We went back andforth, failing to change the other’smind.

A View From the Lecture Hall

Michigan’s program did not randomly assign its own students to
courses using different teaching
models, as conventional education research would dictate. But the
gains in learning that were observed
at Michigan correspond with similar findings about teaching methodologies in physics, which have been
documented by Richard R. Hake, a
professor emeritus of physics at Indiana University at Bloomington.

In fact, the project at Michigan
was modeled on similar work by
physicists, who have been among
the most innovative STEM scholars
in trying new approaches to teaching and testing the results.

One of the most outspoken physicists is Eric Mazur of Harvard University. He has been flipping courses
for 21 years using a method he calls
“peer instruction,” in which students
work in small groups to answer conceptual questions during lectures.
Mr. Mazur recently established a
network of practitioners in the technique.

He began to use peer instruction
after testing his own students on the
force concept inventory, which predates the calculus concept inventory,
and which tests understanding of the
foundations of Newtonian mechanics. Despite his consistently high ratings from students, Mr. Mazur saw
that they were not learning as much
as he thought they were.

“We put a lot of emphasis on the
transfer of information,” Mr. Mazur
said at a recent conference at Harvard on teaching and learning. But

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